Finite Group Databasebeta

← D11×#1703 #14736342

Subgroups — D11×#1703 #14736342

Order 2816.

694 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#487C211yesmaximal, characteristic, complemented
2D11×#476C211yesmaximal, characteristic
3D11×#474C211yesmaximal, characteristic
4D11×#436C211yesmaximal, characteristic
5#13068194C211yesmaximal, characteristic, complemented
6#13068193C211yesmaximal, characteristic, complemented
7#13068192C211yesmaximal, characteristic, complemented
8#13068191C211yesmaximal, characteristic, complemented
9#13068190C211yesmaximal, characteristic, complemented
10#13068189C211yesmaximal, characteristic, complemented
11#13068188C211yesmaximal, characteristic, complemented
12D11×#334C211yesmaximal, characteristic, complemented
13D11×#333C211yesmaximal, characteristic, complemented
14D11×#332C211yesmaximal, characteristic, complemented
15C11×#1703C211yesmaximal, characteristic, complemented
16C2×M16×D11—21no—
17D11×C4⋊Q8C2211yescharacteristic
18D11×C4⋊Q8C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C11×#487C2211yescharacteristic, complemented
21C11×#476C2211yescharacteristic
22C11×#474C2211yescharacteristic
23C11×#436C2211yescharacteristic
24#10622741—21no—
25#10622706C2211yescharacteristic, complemented
26#10622700C2211yescharacteristic
27#10622697C2211yescharacteristic
28#10622694C2211yescharacteristic, complemented
29#10622625C2211yescharacteristic
30#10622621C2211yescharacteristic
31#10622620C2211yescharacteristic
32#10622503—21no—
33D11×#107—21no—
34#10622483—21no—
35D11×#106—21no—
36#10622459C2211yescharacteristic
37#10622455C2211yescharacteristic
38#10622451C2211yescharacteristic
39D11×C4⋊C8C2211yescharacteristic
40D11×C4⋊C8C2211yescharacteristic
41D11×C4⋊C8C2211yescharacteristic
42D11×#103—21no—
43D11×#103—21no—
44#10622405—21no—
45#10622405—21no—
46D11×#102—21no—
47D11×#102—21no—
48#10622374—21no—
49#10622372—21no—
50#10622342—21no—
51D11×C22⋊C8—21no—
52#10622301C2211yescharacteristic
53C4×C8×D11C2211yescharacteristic
54#10622294C2211yescharacteristic, complemented
55C11×#334C2211yescharacteristic, complemented
56C11×#333C2211yescharacteristic, complemented
57C11×#332C2211yescharacteristic, complemented
58#10622185C2211yescharacteristic, complemented
59#10622184C2211yescharacteristic, complemented
60#10622124C2211yescharacteristic, complemented
61#10622120C2211yescharacteristic, complemented
62#10622119C2211yescharacteristic, complemented
63#10622119C2211yescharacteristic, complemented
64#10622118C2211yescharacteristic, complemented
65#10622118C2211yescharacteristic, complemented
66#10622095C2211yescharacteristic, complemented
67C2×Q8×D11—21no—
68C2×Q8×D11—21no—
69C2×D4×D11D411yescharacteristic
70C22×C4×D11—21no—
71C2×C11×M16—21no—
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C4×D4×C11C2311yescharacteristic
75#66997—21no—
76#66997—21no—
77D4×Dic11D411yescharacteristic
78C4×C22⋊D11—21no—
79C2×#4318—21no—
80M16×D11—44no—
81C2×#4313—21no—
82C2×#4313—21no—
83C2×C8×D11—21no—
84C2×C8×D11—21no—
85C2×C8×D11—21no—
86C2×C8×D11D411yescharacteristic
87C2×C8×D11D411yescharacteristic
88#66946D411yescharacteristic
89C4⋊C4×D11—21no—
90C4⋊C4×D11—21no—
91C4⋊C4×D11—21no—
92C4⋊C4×D11—21no—
93C4⋊C4×D11D411yescharacteristic
94#66941—21no—
95#66941—21no—
96#66941—21no—
97#66941—21no—
98(C22⋊D11)⋊C4—21no—
99C22⋊C4×D11—21no—
100C4×D44C2311yescharacteristic
101C42×D11C2311yescharacteristic
102#66922C2311yescharacteristic
103#66922C2311yescharacteristic
104C11×#107—21no—
105C11×#106—21no—
106C11×C4⋊C8C2311yescharacteristic
107C11×C4⋊C8C2311yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×#103—21no—
110C11×#103—21no—
111C11×#102—21no—
112C11×#102—21no—
113C11×C22⋊C8—21no—
114C4×C8×C11C2311yescharacteristic
115#66899—21no—
116#66899—21no—
117#66896—21no—
118#66896—21no—
119C22⋊(C11⋊C8)—21no—
120#66885—21no—
121#66885—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124#66882—21no—
125#66881—21no—
126#66880—21no—
127#66880—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131C8×Dic11D411yescharacteristic
132C8×Dic11D411yescharacteristic
133#66874—21no—
134#66874—21no—
135#66873—21no—
136#66873—21no—
137#66872—21no—
138#66872—21no—
139#66871—21no—
140#66871—21no—
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C2×#1703—111nomaximal, Sylow
146C23×D11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×D4×C11C2×D411yescharacteristic
150C22×C4×C11—21no—
151C2×C22⋊D11—21no—
152C22×Dic11—21no—
153Q8×D11—42no—
154Q8×D11—42no—
155Q8×D11—82no—
156D4×D11—22no—
157D4×D11—22no—
158C2×D44C2×D411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—41no—
165C2×C4×D11—41no—
166C2×C4×D11C2×D411yescharacteristic
167C2×C4×D11C2×D411yescharacteristic
168C2×C4×D11#4111yescharacteristic
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—41no—
172C2×Dic22—41no—
173C11×M16—42no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×D411yescharacteristic
184C11×C22⋊C4—21no—
185C42×C11C2411yescharacteristic
186C22⋊Dic11—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C2×D411yescharacteristic
194Dic11⋊C4—21no—
195Dic11⋊C4—41no—
196Dic11⋊C4—41no—
197Dic11⋊C4—41no—
198Dic11⋊C4—41no—
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201C4×Dic11#4111yescharacteristic
202#4318—42no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208#4313—42no—
209#4313—42no—
210C8×D11—22no—
211C8×D11—22no—
212C8×D11—42no—
213C8×D11—42no—
214C8×D11—42no—
215C2×#487—111no—
216C2×#476—111no—
217C2×#474—111no—
218C2×#436—111no—
219#1703—111no—
220#1703—111no—
221#1703—111no—
222#1703—111no—
223#1703—111no—
224#1703—111no—
225#1703—111no—
226#1703D1111yescharacteristic, direct product factor
227C2×#334—111no—
228C2×#333—111no—
229C2×#332—111no—
230C23×C11—21no—
231C22×D11—21no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11#12111yescharacteristic
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—81no—
239D4×C11—21no—
240D4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C22⋊D11—42no—
250C2×Dic11—21no—
251C2×Dic11—42no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11#12111yescharacteristic
255C2×Dic11#12111yescharacteristic
256C2×Dic11#12111yescharacteristic
257D44—21no—
258D44—21no—
259C4×D11—22no—
260C4×D11—42no—
261C4×D11—41no—
262C4×D11—41no—
263C4×D11—42no—
264C4×D11—82no—
265C4×D11—82no—
266C4×D11#13512yes—
267C4×D11AGL(1,ℤ/8)12yes—
268C4×D11#13712yes—
269C4×D11#13712yes—
270Dic22—41no—
271Dic22—41no—
272Dic22—82no—
273Dic22—82no—
274Dic22—81no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C22×M16—221no—
286C2×C4⋊Q8—111no—
287C2×C4⋊Q8—111no—
288C2×C4×D4—111no—
289#487—111no—
290#487—111no—
291#487—111no—
292#487—221no—
293#487—221no—
294#487C2×D1111yescharacteristic, complemented
295#476—111no—
296#476—111no—
297#476—111no—
298#476—221no—
299#476—221no—
300#476C2×D1111yescharacteristic
301#474—111no—
302#474—111no—
303#474—111no—
304#474—221no—
305#474—221no—
306#474C2×D1111yescharacteristic
307#436—111no—
308#436—111no—
309#436—111no—
310#436—221no—
311#436—221no—
312#436C2×D1111yescharacteristic
313C2×#107—221no—
314C2×#106—221no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×C4⋊C8—111no—
318C2×#103—221no—
319C2×#103—221no—
320C2×#102—221no—
321C2×#102—221no—
322C2×C22⋊C8—221no—
323C2×C4×C8—111no—
324#334—111no—
325#334—111no—
326#334—111no—
327#334C2×D1111yescharacteristic, complemented
328#333—111no—
329#333—111no—
330#333—111no—
331#333C2×D1111yescharacteristic, complemented
332#332—111no—
333#332—111no—
334#332—111no—
335#332C2×D1111yescharacteristic, complemented
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×#12111yescharacteristic
340C2×D11—41no—
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—84no—
344C2×D11#46312yes—
345C2×D11#47012yes—
346C2×D11#47112yes—
347C4×C11—21no—
348C4×C11—41no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11C2×#13511yescharacteristic
352C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
353C4×C11C2×#13711yescharacteristic
354C4×C11C2×#13711yescharacteristic
355Dic11—21no—
356Dic11—41no—
357Dic11—81no—
358Dic11—81no—
359Dic11#46312yes—
360Dic11#47012yes—
361C22×Q8—221no—
362C22×Q8—221no—
363C22×D4—111no—
364C23×C4—221no—
365C2×M16—21no—
366C2×M16—221no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16—444no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375C4⋊Q8—111no—
376C4⋊Q8—111no—
377C4⋊Q8—221no—
378C4⋊Q8—221no—
379C4⋊Q8—221no—
380C4⋊Q8—221no—
381C4⋊Q8—221no—
382C4⋊Q8—221no—
383C4⋊Q8C22×D1111yescharacteristic
384C4⋊Q8C22×D1111yescharacteristic
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—111no—
388C4×D4—221no—
389C4×D4—221no—
390C4×D4C22×D1111yescharacteristic
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C42—111no—
398#107—21no—
399#107—221no—
400#107—221no—
401#107—221no—
402#106—21no—
403#106—221no—
404#106—221no—
405#106—221no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412C4⋊C8C22×D1111yescharacteristic
413C4⋊C8C22×D1111yescharacteristic
414C4⋊C8C22×D1111yescharacteristic
415#103—21no—
416#103—21no—
417#103—221no—
418#103—221no—
419#103—221no—
420#103—221no—
421#103—221no—
422#103—221no—
423#102—21no—
424#102—21no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429#102—221no—
430#102—221no—
431C22⋊C8—21no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434C22⋊C8—221no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8C22×D1111yescharacteristic
439C2×C11—81no—
440C2×C11C2×#46311yescharacteristic
441C2×C11C2×#47011yescharacteristic
442C2×C11C2×#47111yescharacteristic
443D11—81no—
444D11#170314yesdirect product factor
445C24—221no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—441no—
451C2×Q8—441no—
452C2×Q8—442no—
453C2×Q8—442no—
454C2×Q8—882no—
455C2×D4—111no—
456C2×D4—222no—
457C2×D4—222no—
458C2×D4—221no—
459C2×D4D4×D1111yescharacteristic
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—442no—
469C22×C4—442no—
470C22×C4—441no—
471C22×C4—441no—
472M16—42no—
473M16—442no—
474M16—442no—
475M16—442no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—442no—
487C2×C8—442no—
488C2×C8—442no—
489C2×C8D4×D1111yescharacteristic
490C2×C8D4×D1111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—441no—
502C4⋊C4—441no—
503C4⋊C4—441no—
504C4⋊C4—441no—
505C4⋊C4D4×D1111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C42—111no—
511C42—111no—
512C42—111no—
513C42C23×D1111yescharacteristic
514C11C2×#170311yescharacteristic, complemented, Sylow
515C23—21no—
516C23—111no—
517C23—221no—
518C23—442no—
519C23—442no—
520C23—442no—
521Q8—41no—
522Q8—41no—
523Q8—81no—
524Q8—441no—
525Q8—441no—
526Q8—881no—
527Q8—882no—
528Q8—882no—
529D4—21no—
530D4—21no—
531D4—221no—
532D4—221no—
533D4—442no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—112no—
542C2×C4—112no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—111no—
546C2×C4—222no—
547C2×C4—221no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—882no—
556C2×C4—882no—
557C2×C4C2×D4×D1111yescharacteristic
558C2×C4C2×D4×D1111yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—221no—
566C8—221no—
567C8—441no—
568C8—441no—
569C8—441no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—112no—
574C22—112no—
575C22—112no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—884no—
580C22D11×#12111yescharacteristic
581C4—21no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—112no—
586C4—112no—
587C4—221no—
588C4—441no—
589C4—881no—
590C4—881no—
591C4D11×#13511yescharacteristic
592C4D11×AGL(1,ℤ/8)11yescharacteristic
593C4D11×#13711yescharacteristic
594C4D11×#13711yescharacteristic
595C2—81no—
596C2—114no—
597C2—881no—
598C2D11×#46311yescharacteristic
599C2D11×#47011yescharacteristic
600C2D11×#47111yescharacteristic
subgroupG/H
centerC22D11×#121
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1703C2
socleC22×C11C2×#121
prime radicalC2×D4×D11D4
hypercenter#1703D11
hypocenterC11C2×#1703
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #1703

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. D11×#487C2semidirect
5. #13068194C2semidirect
6. #13068193C2semidirect
7. #13068192C2semidirect
8. #13068191C2semidirect
9. #13068190C2semidirect
10. #13068189C2semidirect
11. #13068188C2semidirect
12. D11×#334C2semidirect
13. D11×#333C2semidirect
14. D11×#332C2semidirect
15. C11×#1703C2semidirect
20. C11×#487C22semidirect
25. #10622706C22semidirect
28. #10622694C22semidirect
54. #10622294C22semidirect
55. C11×#334C22semidirect
56. C11×#333C22semidirect
57. C11×#332C22semidirect
58. #10622185C22semidirect
59. #10622184C22semidirect
60. #10622124C22semidirect
61. #10622120C22semidirect
62. #10622119C22semidirect
63. #10622119C22semidirect
64. #10622118C22semidirect
65. #10622118C22semidirect
66. #10622095C22semidirect
226. #1703D11direct (N × H)
294. #487C2×D11semidirect
327. #334C2×D11semidirect
331. #333C2×D11semidirect
335. #332C2×D11semidirect
444. D11#1703direct (N × H)
514. C11C2×#1703semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D11×#4872
D11×#4762
D11×#4742
D11×#4362
#130681942
#130681932
#130681922
#130681912
#130681902
#130681892
#130681882
D11×#3342
D11×#3332
D11×#3322
C11×#17032
C2×#170311